All batteries charging on shore power?

[dogsandcats]

I know this has been asked before on the site but I don't understand the responses. I have a 2006 E350 6.0 with a Tripp Lite inverter. When I'm plugged into shore power, are all the batteries being charged automatically or is there an on/off switch or whatever to include the vehicle battery in the charging process? If there's a switch or button for this, what does it look like and where is it likely to be and, what position should it be switched too for shore power charging or back to the alternator when driving? Thanks